High School

We appreciate your visit to The height of adult males on a given South Pacific Island is approximately normally distributed with a mean of 65 inches and a standard deviation. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

The height of adult males on a given South Pacific Island is approximately normally distributed with a mean of 65 inches and a standard deviation of 4 inches. Calculate the probability for each of the following scenarios:

A. Taller than 64 inches
B. Shorter than 62 inches
C. Between 64 inches and 68 inches
D. Between 58 and 68 inches
E. Taller than 58 inches

Answer :

Answer:

a) 0.59871

b) 0.22663

e) 0.95994

Step-by-step explanation:

The height of adult males on a given South Pacific Island is approximately normally distributed with mean 65 inches and standard deviation of 4 inches.

We solve using z score

z = (x-μ)/σ, where

x is the raw score

μ is the population mean = 65 inches

σ is the population standard deviation = 4 inches

a). Taller than 64 inches

This means x > 64

Hence,

64 - 65/4

=- 1/4 = -0.25

P-value from Z-Table:

P(x<64) = 0.40129

P(x>64) = 1 - P(x<64) = 0.59871

b.) shorter than 62 inches

Hence,

62 - 65/4

=- 3/4 =- 0.75

P-value from Z-Table:

P(x<62) = 0.22663

c.) between 64 inches and 68 inches

Hence,

for 64 inches

64 - 65/4

=- 1/4 = -0.25

P-value from Z-Table:

P(x = 64) = 0.40129

For 68 inches

Hence,

68 - 65/4

= 3/4= 0.75

P-value from Z-Table:

P(x = 68) = 0.77337

d.) between 58 and 68 inches

e.) taller than 58 inches

Hence,

58 - 65/4

= -6/4 = -1.5

P-value from Z-Table:

P(x<58) = 0.040059

P(x>58) = 1 - P(x<58) = 0.95994

Thanks for taking the time to read The height of adult males on a given South Pacific Island is approximately normally distributed with a mean of 65 inches and a standard deviation. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada